The chiral vortical effect and mixed gravitational anomaly have the same coefficient, which follows from free theory and holographic examples, see e.g. Ref. [1]}, [2]}, [3]}, [4]} and references therein. Above, we discussed this anomalous current induced by chemical potential from the chiral anomaly with coefficient \(c_{\chi }\mu ^2\) , below the \(\propto T^2\)  term with coefficient \(d_\chi \)  is discussed via the response to \(\delta g_{ti}\)  around flat space and its relation to the torsional anomaly. The connection is reviewed below at level of linear response Kubo formula for free fermions.
